Imaginary Numbers

We usually imagine all the numbers as occupying a number line, with zero at the center, the negative numbers at the left, and the positive numbers at the right. The notion of "imaginary" or "complex" numbers generalizes this picture. Rather than existing on such a number line, complex numbers exist in a number plane, a two-dimensional arena. QCI Theory combines imaginary numbers with the mathematics of quantum physics.

Throughout history, mankind has generalized the concept of "number", first from the integers to the fractions, then to zero and negative numbers, and finally to the "irrationals" like pi and the square root of two. Imaginary numbers follow in the light of previous generalizations, consisting of numbers existing outside the number line itself. The imaginaries link algebra with geometry, allowing numbers to represent points in the plane.

The imaginary numbers are simply the square roots of negative numbers. A positive number multiplied by itself is clearly positive, and the same is true of a negative number: therefore, the square root of a negative number cannot, itself, be positive, negative, or zero. As such, it must exist outside the number line.

On the number line, there are only two distinct directions: left and right. In the expanded plane of the imaginary numbers, however, there are an infinity of different directions: north, south, east, west, northeast, and so on. When imaginary numbers are combined with quantum physics, this increased variety results in a description of an infinity of alternate universes.